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P(x) = x^3 + (t - 1)x^2 - (t + 3)x + 1

Source: 2011 Cuba MO 2.1

September 17, 2024
algebrapolynomialinequalities

Problem Statement

Let P(x)=x3+(t−1)x2−(t+3)x+1P(x) = x^3 + (t - 1)x^2 - (t + 3)x + 1. For what values of real tt the sum of the squares and the reciprocals of the roots of P(x) P(x) is minimum?
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